Yusmichad Yusdja, staff researcher at the Center for Research and Social and Economic Development of Agriculture IPB
Hundreds of years ago, people only Knew the 9 symbol numbers 1, 2, 2, 3, 5, 6, 7, 8, and 9. Then, come the number 0, so the number of symbol numbers into 10 pieces. It is unknown WHO's the creator of the number 0, the only historical evidence shows That the number 0, first discovered in ancient Egyptian times.
At That time only as a symbol number zero. In modern times, the number zero is Used not only as a symbol, but Also as the number WHO participated in mathematical operations. Now, use the number zero has infiltrated deep into the joints of human life.
Counting system is no longer possible to ignore the presence of zero, although zero-one made a mess of logic. Let's see.
Zero, cause crashes
Lessons about the number zero, from ancient times Until now always cause confusion for students and students, and even the user community. Why? Is not zero-one represents something That does not exist and That nothing was there, namely zero.
Who is not confused? EACH time the number zero appears in mathematics there is always a weird idea. Like the idea if something is multiplied by 0 then Becomes not exist. Could it be 5 * 0 to not exist? (* Is multiplication). This idea makes people frustrated. Is zero magician?
Worse yet-confused-why Would increase is 5 +0 = 5 and 5 * 0 = 5 as well? Indeed Such a rule, Because of zero in multiplication is the identity numbers are equal to 1. So 5 * 0 = 5 * 1. However, it is true That Also 5 * 0 = 0. Waw. What about 5o = 1, but 50o = 1, too?
a, never mind. Another rule of zero the which is mysterious Also Is That a number is divided by zero if not defined. That is, whatever number That cans not be divided by zero. Sophisticated computer earnest Suddenly somehow die if a sudden meeting with a zero divisor. Computers are ordered to stop to think if he met the divisor is zero.
Numbers zero: homeless
Numbers have been Prepared based on the hierarchy by a single straight line. At the starting point is the number zero, then number 1, 2, and so on. Greater numbers on the right and a Smaller numbers on the left. The farther to the right will from some events this Greater number.
Based on the degree of hierarchy (and bureaucracy numbers), a person walking from point 0 if continually Towards Greater numbers to the right earnest reach the numbers the which do not infinite. However, that person May Also come to the point 0 again.
Is not this world round? Could it be? Columbus Did not Say That if he kept sailing Until Would he return to Europe?
Another. If someone departs from zero, it is not possible Until the number 4 without first passing numbers 1, 2, and 3. But more strange is the question of possible Could someone go from point zero?
Obviously not, Because it is not the point of zero point something That does not exist? Strange and hard to believe? Let's look Further.
If in Between two numbers or Between two points there is a segment. EACH number has a vertebra. If this segment is cut into pieces and then a black circle dots Moved into the middle segment, was number 0 does not have sections. Thus, the number zero was in the clouds.
Numbers zero alias has no homeless shelter. That is why, why the number zero Should Be attached to another number, for example, in figure 1 form the number 10, 100, 109, 10 403 and so forth. So, one cans never go from zero to the number 4. We must Depart from the 1.
Easy, but wrong
The teacher ACKs the Ani describes a geometric lines of the equation 3x +7 y = 25. Ani think That to get a line That needed two points from end to end. However, after the count is calculated, it turns out there's only one point passed the line, ie, point A (6, 1), for x = 6 and y = 1. So That Annie cans not make the line.
The teacher warned That using the number zero. Yes, that's the way out. First, give y = 0 obtained by x = (25-0) / 3 = 8 (rounded), is the first point, B (8.0). Furthermore, given x = 0 obtained by y = (25-3.0) / 7 = 4 (rounded), is the second point C (0,4). Line BC, is the line in question. However, how disappointed the teacher, Because the line was not through point A. Thus, the BC line is wrong.
Ani defend themselves That the error was very small and cans be ignored. Teachers stated That it was not a small amount of Mistakes, but Nowhere Is That correct? Is not the line BC cans be made through the point A? Said the teacher, use the number zero in the right way.
How do We have to help Annie make the correct line is? Easy, says consultant Mathematics. At first the value of 25 in 3x +7 y Should Be Replaced with the result of multiplying 3 and 7 That obtained 3x +7 y = 21.
Furthermore, in the new equation, given y = 0 obtained x = 21 / 3 = 7 (without rounding) was the first point P (6.1). Then give the value x = 0 obtained by y = 21 / 7 = 3 (without rounding), that's the second point Q (0, 3).
The line PQ is a line parallel to the line to be searched, namely 3x +7 y = 25. Through point A drag line parallel to PQ obtained P1Q1 line. Well, that's it. The students have found the correct line thanks to the help number zero.
However, the teacher was very disappointed Because no one Actually Had the correct line. Is not in the equation 3x1 +7 x2 = 25 'there is only one solution That point is point A, the which means the equation 3x1 +7 x2-shaped it's just a point?
Even in the equation 3x1 +7 x2 = 21 does not exist a point no matter Who is in line PQ. Therefore, the line PQ in the system of integers, does not really exist. Strange, the number zero has deceived us. That fact, the equation does not always form a line.
Moving, but stationary
Numbers do not only consist of integers, but Also there is a decimal number, Among others, from 0.1, 0.01, 0,001; and so strong-as strong as We can call it up so small. Since very little cans no longer be Called or not infinite and in the end it is Considered zero.
But this idea turned out was confusing Because if an infinitely small number treated as zero then means zero is the smallest number? In fact, the zero represents something That does not exist? Waw. That's it.
Based on the concept of decimals and continuous, then We use the number line is not That Simple Because Between two numbers there is always a number to three. If someone jumped from number 1 to number 2, but with the condition have to jump over Them first to the nearest decimal, can he?
What is the nearest decimal before it reached the number 2? It Could Be the number 1 / 2. However, you Should not jump to number 1 / 2 Because there is still a Smaller numbers, namely 1 / 4.
So there is always a number That more closely ... namely 0.1 and then there are 0.01, 0.001, ..., 0.000001. and so on, so That eventually the number closest to the number 1 is so small That number is Considered to be zero. Because the nearest number is zero alias does not exist, then you cans never jump to number 2?
Hundreds of years ago, people only Knew the 9 symbol numbers 1, 2, 2, 3, 5, 6, 7, 8, and 9. Then, come the number 0, so the number of symbol numbers into 10 pieces. It is unknown WHO's the creator of the number 0, the only historical evidence shows That the number 0, first discovered in ancient Egyptian times.
At That time only as a symbol number zero. In modern times, the number zero is Used not only as a symbol, but Also as the number WHO participated in mathematical operations. Now, use the number zero has infiltrated deep into the joints of human life.
Counting system is no longer possible to ignore the presence of zero, although zero-one made a mess of logic. Let's see.
Zero, cause crashes
Lessons about the number zero, from ancient times Until now always cause confusion for students and students, and even the user community. Why? Is not zero-one represents something That does not exist and That nothing was there, namely zero.
Who is not confused? EACH time the number zero appears in mathematics there is always a weird idea. Like the idea if something is multiplied by 0 then Becomes not exist. Could it be 5 * 0 to not exist? (* Is multiplication). This idea makes people frustrated. Is zero magician?
Worse yet-confused-why Would increase is 5 +0 = 5 and 5 * 0 = 5 as well? Indeed Such a rule, Because of zero in multiplication is the identity numbers are equal to 1. So 5 * 0 = 5 * 1. However, it is true That Also 5 * 0 = 0. Waw. What about 5o = 1, but 50o = 1, too?
a, never mind. Another rule of zero the which is mysterious Also Is That a number is divided by zero if not defined. That is, whatever number That cans not be divided by zero. Sophisticated computer earnest Suddenly somehow die if a sudden meeting with a zero divisor. Computers are ordered to stop to think if he met the divisor is zero.
Numbers zero: homeless
Numbers have been Prepared based on the hierarchy by a single straight line. At the starting point is the number zero, then number 1, 2, and so on. Greater numbers on the right and a Smaller numbers on the left. The farther to the right will from some events this Greater number.
Based on the degree of hierarchy (and bureaucracy numbers), a person walking from point 0 if continually Towards Greater numbers to the right earnest reach the numbers the which do not infinite. However, that person May Also come to the point 0 again.
Is not this world round? Could it be? Columbus Did not Say That if he kept sailing Until Would he return to Europe?
Another. If someone departs from zero, it is not possible Until the number 4 without first passing numbers 1, 2, and 3. But more strange is the question of possible Could someone go from point zero?
Obviously not, Because it is not the point of zero point something That does not exist? Strange and hard to believe? Let's look Further.
If in Between two numbers or Between two points there is a segment. EACH number has a vertebra. If this segment is cut into pieces and then a black circle dots Moved into the middle segment, was number 0 does not have sections. Thus, the number zero was in the clouds.
Numbers zero alias has no homeless shelter. That is why, why the number zero Should Be attached to another number, for example, in figure 1 form the number 10, 100, 109, 10 403 and so forth. So, one cans never go from zero to the number 4. We must Depart from the 1.
Easy, but wrong
The teacher ACKs the Ani describes a geometric lines of the equation 3x +7 y = 25. Ani think That to get a line That needed two points from end to end. However, after the count is calculated, it turns out there's only one point passed the line, ie, point A (6, 1), for x = 6 and y = 1. So That Annie cans not make the line.
The teacher warned That using the number zero. Yes, that's the way out. First, give y = 0 obtained by x = (25-0) / 3 = 8 (rounded), is the first point, B (8.0). Furthermore, given x = 0 obtained by y = (25-3.0) / 7 = 4 (rounded), is the second point C (0,4). Line BC, is the line in question. However, how disappointed the teacher, Because the line was not through point A. Thus, the BC line is wrong.
Ani defend themselves That the error was very small and cans be ignored. Teachers stated That it was not a small amount of Mistakes, but Nowhere Is That correct? Is not the line BC cans be made through the point A? Said the teacher, use the number zero in the right way.
How do We have to help Annie make the correct line is? Easy, says consultant Mathematics. At first the value of 25 in 3x +7 y Should Be Replaced with the result of multiplying 3 and 7 That obtained 3x +7 y = 21.
Furthermore, in the new equation, given y = 0 obtained x = 21 / 3 = 7 (without rounding) was the first point P (6.1). Then give the value x = 0 obtained by y = 21 / 7 = 3 (without rounding), that's the second point Q (0, 3).
The line PQ is a line parallel to the line to be searched, namely 3x +7 y = 25. Through point A drag line parallel to PQ obtained P1Q1 line. Well, that's it. The students have found the correct line thanks to the help number zero.
However, the teacher was very disappointed Because no one Actually Had the correct line. Is not in the equation 3x1 +7 x2 = 25 'there is only one solution That point is point A, the which means the equation 3x1 +7 x2-shaped it's just a point?
Even in the equation 3x1 +7 x2 = 21 does not exist a point no matter Who is in line PQ. Therefore, the line PQ in the system of integers, does not really exist. Strange, the number zero has deceived us. That fact, the equation does not always form a line.
Moving, but stationary
Numbers do not only consist of integers, but Also there is a decimal number, Among others, from 0.1, 0.01, 0,001; and so strong-as strong as We can call it up so small. Since very little cans no longer be Called or not infinite and in the end it is Considered zero.
But this idea turned out was confusing Because if an infinitely small number treated as zero then means zero is the smallest number? In fact, the zero represents something That does not exist? Waw. That's it.
Based on the concept of decimals and continuous, then We use the number line is not That Simple Because Between two numbers there is always a number to three. If someone jumped from number 1 to number 2, but with the condition have to jump over Them first to the nearest decimal, can he?
What is the nearest decimal before it reached the number 2? It Could Be the number 1 / 2. However, you Should not jump to number 1 / 2 Because there is still a Smaller numbers, namely 1 / 4.
So there is always a number That more closely ... namely 0.1 and then there are 0.01, 0.001, ..., 0.000001. and so on, so That eventually the number closest to the number 1 is so small That number is Considered to be zero. Because the nearest number is zero alias does not exist, then you cans never jump to number 2?
Mystery Numbers : Zero